This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064999 #48 Dec 22 2023 12:11:12
%S A064999 1,3,9,21,41,71,113,169,241,331,441,573,729,911,1121,1361,1633,1939,
%T A064999 2281,2661,3081,3543,4049,4601,5201,5851,6553,7309,8121,8991,9921,
%U A064999 10913,11969,13091,14281,15541,16873,18279,19761,21321,22961,24683
%N A064999 Partial sums of sequence (essentially A002378): 1, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...
%C A064999 Equals triangle A144328 * [1, 2, 3, ...]. - _Gary W. Adamson_, Sep 18 2008
%C A064999 a(n) is the number of parking functions of size n+1 avoiding the patterns 123 and 312. - _Lara Pudwell_, Apr 10 2023
%H A064999 Harry J. Smith, <a href="/A064999/b064999.txt">Table of n, a(n) for n = 0..1000</a>
%H A064999 Ayomikun Adeniran and Lara Pudwell, <a href="https://doi.org/10.54550/ECA2023V3S3R17">Pattern avoidance in parking functions</a>, Enumer. Comb. Appl. 3:3 (2023), Article S2R17.
%H A064999 Kassie Archer, Ethan Borsh, Jensen Bridges, Christina Graves, and Millie Jeske, <a href="https://arxiv.org/abs/2312.05145">Cyclic permutations avoiding patterns in both one-line and cycle forms</a>, arXiv:2312.05145 [math.CO], 2023. See p. 2.
%H A064999 Franck Ramaharo, <a href="https://arxiv.org/abs/1712.06543">Enumerating the states of the twist knot</a>, arXiv:1712.06543 [math.CO], 2017.
%H A064999 Franck Ramaharo, <a href="https://arxiv.org/abs/1802.07701">Statistics on some classes of knot shadows</a>, arXiv:1802.07701 [math.CO], 2018.
%H A064999 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A064999 a(n) = A007290(n+2) + 1 = (n^3 + 3*n^2 + 2*n + 3)/3.
%F A064999 a(0) = 1, a(n) = n*(n+1) + a(n-1) for n > 1. - _Gerald McGarvey_, Sep 26 2004
%F A064999 O.g.f.: (1 - x + 3x^2 - x^3)/(1 - x)^4.
%p A064999 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^2-n od: seq(a[n], n=0..42); # _Zerinvary Lajos_, Jun 05 2008
%t A064999 Table[(x^3 - x + 3)/3, {x, 1, 100}] (* _Artur Jasinski_, Feb 14 2007 *)
%t A064999 LinearRecurrence[{4, -6, 4, -1}, {1, 3, 9, 21}, 50] (* _Vincenzo Librandi_, Feb 28 2016 *)
%o A064999 (PARI) { for (n=0, 1000, if (n, a+=n*(n + 1), a=1); write("b064999.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 03 2009
%o A064999 (PARI) a(n) = (n^3+3*n^2+2*n+3)/3; \\ _Altug Alkan_, May 16 2018
%o A064999 (Magma) [(n^3+3*n^2+2*n+3)/3: n in [0..50]]; // _Vincenzo Librandi_, Feb 28 2016
%Y A064999 Cf. A002378, A007290.
%Y A064999 Cf. A144328. - _Gary W. Adamson_, Sep 18 2008
%K A064999 easy,nonn
%O A064999 0,2
%A A064999 Klaus E. Kastberg (kastberg(AT)hotkey.net.au), Oct 31 2001
%E A064999 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Nov 12 2001